Waves

Waveform

Obtained by plotting instantaneous values of a time-varying quantity against time.

Periodic Waveform

A pattern repeats after $T$ time. Periodic time is $T$ and frequency $f$ is $\frac{1}{T}$.

Alternating Waveform

A waveform that changes in magnitude and direction with time. Is also a periodic waveform.

Symmetric Waveform

A periodic waveform that is symmetric about the time axis.

Sinusoidal Waves

An alternating and symmetric waveform. Same as $\sin\theta$ vs $\theta$ (in rad). Also called sine waves or sinusoid.

$$y=A\sin(\omega{t}+\phi)$$

When $\phi$ is: $$

• $\gt{0}$ - the wave is said to be leading by $\phi$
• $=0$ - the wave is the reference
• $\lt{0}$ - the wave is said to be lagging by $\phi$

Sinusoidal voltages can be easily generated using rotating machines.

Complex Waveforms

Periodic non-sinusoidal waveforms can be split into its fundamental and harmonics.

Fundamental Waveform

$$f_0=f_{\text{complex}}$$

Harmonics

Sine waves with higher frequencies which is a multiple of $f_0$.$$

$$f_{\text{harmonic}} = n\cdot f_0\;;\,n\in\mathbb{Z}$$

Harmonics are grouped into:

• odd harmonic when $n$ is odd.
• even harmonic when $n$ is even.